Solution: Crack Width Check

1.1 Effective Depth

• Assume effective depth d = 450mm (cover 25mm, bar dia 16mm)

1.2 Neutral Axis Calculation

• Neutral axis depth (x_u) is calculated using the equilibrium equation:
• 0.36 × f_ck × b × x_u = 0.87 × f_y × A_s
• Substitute values: 0.36 × 30 × 300 × x_u = 0.87 × 500 × 603.19
• Solve for x_u: x_u = (0.87 × 500 × 603.19) / (0.36 × 30 × 300) = 242.2 mm
• Lever arm (z) = d - 0.42 × x_u = 450 - 0.42 × 242.2 = 348.1 mm

2.1 Steel Stress

• Steel stress (f_s) is calculated as:
• f_s = M / (A_s × z)
• Substitute values: f_s = (35 × 10⁶) / (603.19 × 348.1) = 165.2 MPa

2.2 Surface Crack Width

• Surface crack width (w_max) is calculated using the formula:
• w_max = 0.21 × s × (f_s - 120) / (d - x_u)
• Substitute values: w_max = 0.21 × 100 × (165.2 - 120) / (450 - 242.2)
• w_max = 0.21 × 100 × 45.2 / 207.8 = 0.046 mm

3.1 Permissible Limit

• Permissible crack width = 0.300 mm
• Calculated crack width = 0.046 mm